[Paper Review] Choosing Colors for Geometric Graphs via Color Space Embeddings

Michael B. Dillencourt, David Eppstein+1 more|ArXiv.org|Sep 7, 2006

Data Visualization and Analytics11 references4 citations

TL;DR

This paper proposes a novel method for assigning visually distinct colors to vertices in geometric graphs by embedding the graph in perceptually uniform color spaces like Lab, optimizing color differences between adjacent vertices. Using force-directed and gradient descent algorithms in perceptually accurate color spaces, the approach significantly improves color separation for adjacent nodes compared to random or sRGB-based methods, with Lab space yielding superior results due to better alignment with human color perception.

ABSTRACT

Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored: assigning display colors to the graph's vertices. We study the additional aesthetic criterion of assigning distinct colors to vertices of a geometric graph so that the colors assigned to adjacent vertices are as different from one another as possible. We formulate this as a problem involving perceptual metrics in color space and we develop algorithms for solving this problem by embedding the graph in color space. We also present an application of this work to a distributed load-balancing visualization problem.

Motivation & Objective

• To address the overlooked challenge of assigning perceptually distinct colors to vertices in geometric graphs after geometric embedding.
• To develop a bi-criterion coloring strategy that ensures all colors are distinct and adjacent vertices have maximally different colors.
• To model color difference using perceptual metrics in color space, particularly Lab, to better align with human visual perception.
• To apply the method to a distributed load-balancing visualization problem, demonstrating practical utility.
• To provide a framework for color assignment that leverages adjacency information, a gap in prior data visualization and graph drawing research.

Proposed method

• Embed the geometric graph in a perceptual color space (e.g., Lab) to model color differences based on human visual perception.
• Use a force-directed algorithm to position graph vertices in color space such that adjacent vertices are maximally separated.
• Apply gradient descent optimization to minimize a quality function based on Euclidean distance in color space, maximizing minimum color differences across edges.
• Restrict color assignments to a convex hull of extreme sRGB colors in Lab space to ensure display compatibility while preserving perceptual uniformity.
• Use rescaling from neutral gray (50,0,0 in Lab) to project out-of-gamut colors back into the visible color space.
• Leverage planar duality to extend the method to map coloring problems, where regions sharing a border are treated as adjacent vertices.

Experimental results

Research questions

• RQ1 Can adjacency information in geometric graphs be used to systematically assign more visually distinct colors to adjacent vertices?
• RQ2 How does using perceptually uniform color spaces like Lab improve color separation compared to standard sRGB space?
• RQ3 To what extent does the choice of color space and optimization method affect the visual distinguishability of adjacent vertices in graph drawings?
• RQ4 Can this method be effectively applied to real-world visualization problems such as load-balancing in distributed systems?
• RQ5 How does the algorithm perform in comparison to random or uniform color assignment in terms of perceptual color difference?

Key findings

• The Lab color space produced significantly better color separation than sRGB, with fewer difficult-to-distinguish nonadjacent color pairs.
• The gradient descent algorithm in Lab space successfully generated a diverse set of well-saturated, perceptually distinct colors for adjacent vertices.
• The method reduced the number of visually similar adjacent color pairs compared to random or sRGB-based assignments.
• Nonadjacent color pairs such as dark pinks and dark green vs. black remained challenging, but were fewer and less severe in Lab space.
• The algorithm’s performance was robust despite the random initialization, with consistent results across runs due to the optimization process.
• The approach was successfully applied to a distributed load-balancing visualization, demonstrating practical utility in real-world data visualization.